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Chap 1-1
Statistics for Managers Using Microsoft Excel®
7th Edition
Chapter 1
Defining & Collecting Data
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-2
Learning Objectives
In this chapter you learn:
The types of variables used in statistics How to collect data The different ways to collect a sample About the types of survey errors
Types of Variables
Categorical (qualitative) variables have values that can only be placed into categories, such as “yes” and “no.”
Numerical (quantitative) variables have values that represent quantities. Discrete variables arise from a counting process Continuous variables arise from a measuring process
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-3
DCOVA
Types of Variables
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-4
Variables
Categorical Numerical
Discrete Continuous
Examples:
Marital Status Political Party Eye Color (Defined categories) Examples:
Number of Children Defects per hour (Counted items)
Examples:
Weight Voltage (Measured characteristics)
DCOVA
Chap 1-5
Data Is Collected From Either A Population or A Sample
POPULATION
A population consists of all the items or individuals about which you want to draw a conclusion. The population is the “large group”
SAMPLE
A sample is the portion of a population selected for analysis. The sample is the “small group”
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-6
Population vs. Sample
Population Sample
All the items or individuals about which you want to draw conclusion(s)
A portion of the population of items or individuals
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
Data Cleaning Is Often A Necessary Activity When Collecting Data
Often find “irregularities” in the data Typographical or data entry errors Values that are impossible or undefined Missing values Outliers
When found these irregularities should be reviewed
Many statistical software packages will handle irregularities in an automated fashion (Excel does not)
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-7
Chap 1-8
Types of Samples
Samples
Non-Probability Samples
Judgment
Probability Samples
Simple Random
Systematic
Stratified
Cluster
Convenience
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-9
Types of Samples:Nonprobability Sample
In a nonprobability sample, items included are chosen without regard to their probability of occurrence. In convenience sampling, items are selected based
only on the fact that they are easy, inexpensive, or convenient to sample.
In a judgment sample, you get the opinions of pre-selected experts in the subject matter.
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-10
Types of Samples:Probability Sample
In a probability sample, items in the sample are chosen on the basis of known probabilities.
Probability Samples
Simple Random Systematic Stratified Cluster
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-11
Probability Sample:Simple Random Sample
Every individual or item from the frame has an equal chance of being selected
Selection may be with replacement (selected individual is returned to frame for possible reselection) or without replacement (selected individual isn’t returned to the frame).
Samples obtained from table of random numbers or computer random number generators.
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-12
Selecting a Simple Random Sample Using A Random Number Table
Sampling Frame For Population With 850
Items
Item Name Item #Bev R. 001
Ulan X. 002
. .
. .
. .
. .
Joann P. 849
Paul F. 850
Portion Of A Random Number Table49280 88924 35779 00283 81163 0727511100 02340 12860 74697 96644 8943909893 23997 20048 49420 88872 08401
The First 5 Items in a simple random sample
Item # 492Item # 808Item # 892 -- does not exist so ignoreItem # 435Item # 779Item # 002
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-13
Decide on sample size: n Divide frame of N individuals into groups of k
individuals: k=N/n Randomly select one individual from the 1st
group Select every kth individual thereafter
Probability Sample:Systematic Sample
N = 40n = 4k = 10
First Group
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-14
Probability Sample:Stratified Sample
Divide population into two or more subgroups (called strata)
according to some common characteristic
A simple random sample is selected from each subgroup, with
sample sizes proportional to strata sizes
Samples from subgroups are combined into one This is a common technique when sampling population of voters,
stratifying across racial or socio-economic lines.
Population
Divided
into 4
strata
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-15
Probability SampleCluster Sample
Population is divided into several “clusters,” each representative of the population
A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be
chosen from a cluster using another probability sampling technique A common application of cluster sampling involves election exit polls,
where certain election districts are selected and sampled.
Population divided into 16 clusters. Randomly selected
clusters for sample
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-16
Probability Sample:Comparing Sampling Methods
Simple random sample and Systematic sample Simple to use May not be a good representation of the population’s
underlying characteristics Stratified sample
Ensures representation of individuals across the entire population
Cluster sample More cost effective Less efficient (need larger sample to acquire the same
level of precision)
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-17
Types of Survey Errors
Coverage error or selection bias Exists if some groups are excluded from the frame and have
no chance of being selected
Nonresponse error or bias People who do not respond may be different from those who
do respond
Sampling error Variation from sample to sample will always exist
Measurement error Due to weaknesses in question design, respondent error, and
interviewer’s effects on the respondent (“Hawthorne effect”)
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Chap 1-18
Types of Survey Errors
Coverage error
Nonresponse error
Sampling error
Measurement error
Excluded from frame
Follow up on nonresponses
Random differences from sample to sample
Bad or leading question
(continued)
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc.
DCOVA
Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-19
Chapter Summary
In this chapter we have discussed:
The types of variables used in statistics How to collect data The types of survey errors
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Statistics for Managers Using Microsoft Excel® 7e Copyright ©2014 Pearson Education, Inc. Chap 1-20